Mathematics: Kate is solving x^2 + x-2=0 by completing the square her first two steps are shown step1 x^2 + x=2 step 2 x^2 +x+1/4=2+1/4 what is step 3 and 4

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Kate is solving x^2 + x-2=0 by completing the square

cjstablet04

21.01.2022

Therefore,

$x=1\ \ or\ \ x = -2$

Step-by-step explanation:

Kate is solving by completing the square.

$x^{2} + x-2=0$

Step 1 : Adding 2 to bothe sides we get

$x^{2} + x=2$

Step 2 : Add $(\dfrac{1}{2}\(coefficient\ of\ x))^{2}=\dfrac{1}{4}$

$x^{2} +x+\dfrac{1}{4}=2+\dfrac{1}{4}$

Step 3 : Applying (A+B)² = A² +2AB + B²

$(x+\dfrac{1}{2})^{2}=\dfrac{9}{4}$

Step 4 : Square Rooting

$(x+\dfrac{1}{2}=\pm \sqrt{\dfrac{9}{4}}=\pm \dfrac{3}{2}$

Step 5 : Substituting we get

$x+\dfrac{1}{2}=\dfrac{3}{2}\ \ or\ \ x+\dfrac{1}{2}=-\dfrac{3}{2}\\\\x=\dfrac{2}{2}=1\ \ or\ \ x=\dfrac{-4}{2}=-2$

Therefore,

$x=1\ \ or\ \ x = -2$

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